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Absolutely, and there's also the fact that even though his little brother cares about him, even he calls him trash one or two times (maybe because he's gotten used to hearing it). We also don't know much about the mother, she seems to be a single mother, but all I can tell is that she works a lot.
It's also implied that there was some sort of traumatic experience for Minato in school. When they show his yearbook(?) where his classmates wrote that he sucks and they'll never forgive him for not winning (some fucking inconsequential) competition in school. I wonder if that was all or if that type of event repeated itself while he grew up and nobody set that straight.
I know I'm probably looking too deep into this (XD), but I really think the story (specially because it had some really good and unique aspects) would have benefited so much from having some more background and fleshing out of the characters. Also, as a side note, I think maybe Minato is slightly on the spectrum? maybe? or maybe it's just some cheap supposition on my part to explain some of his behaviors as a kid.
I feel like this needs a second volume. I wish the author would have delved more into Minato's sense of self, it really bothers me that he would think of himself as trash. I don't care that he starts like that, but by the end I feel like he hasn't dealt with that perception. Another volume would probably allow the author to flesh out more both main characters. I really loved what the author tried to do here, the theme is great and has a different angle compared to other yaoi.